Perturbation analysis of the maximal solution of the matrix equation X+A*X-1 A = P

摘要

Consider the nonlinear matrix equation X + A*X(-1)A = P, where A, P are n x n complex matrices with P Hermitian positive definite, and A* denotes the conjugate transpose of a matrix A. In this paper a perturbation bound for the maximal solution of the matrix equation and a computable error bound for approximate solutions are derived by using an elegant property of the maximal solution. The results are illustrated by using numerical examples. (C) 2001 Elsevier Science Inc. All rights reserved. [References: 7]